中文摘要：

针对传统的光束整形算法在设计位相型衍射光学元件时效果差的缺点，本文提出了一种适合于位相型衍射光学元件设计的新混合算法。该混合算法是将变尺度BFGS算法融入遗传算法中，其中变尺度BFGS算法主要用于局部搜索，同时将罚函数优化准则用于成本函数的构造中。相比于传统的优化算法，该混合算法具有效率高、收敛快和稳定性好等优点。作为一个设计实例，我们分别将传统模拟退火算法和该混合算法应用到高斯光束整形中，进行了数值模拟，为了考察该混合算法的可靠性，设定了衍射效率和信噪比两个技术指标。设计结果表明：该混合算法收敛速度快，设计效费比优，仅需少量的迭代次数就能达到高衍射效率和高信噪比的要求。用该混合算法设计的衍射光学元件，能极大地改善整形效果，在均匀性要求较高的场合有广泛的应用前景。

英文摘要：

To optimize the effect of conventional beam shaping algorithm for designing Phase Diffractive Optical Elements （PDOE）, a new hybrid algorithm is presented. It combines the Genetic Algorithm （GA） with transformable scale BFGS （Broyden, Fletcher, Goldfarb, Shanno） algorithm, and penalty function is also used in the cost function conformation. The hybrid algorithm has the global nature of the genetic algorithm as well as the local improvement capabilities of the BFGS algorithm. Compared with other beam shaping algorithms, it has good efficiency, good convergence property and good stability. As a design example, both the conventional simulated annealing algorithm and hybrid algorithm are used into Gaussian beam shaping. To review the reliability of two algorithms, two indexes of diffractive efficiency and Signal-to-noise Ratio （SNR） are considered in numerical simulation. The design results show that hybrid algorithm has good convergence speed and cost function. It can acquire good diffractive efficiency and SNR with only a small quantity of iterative numbers. The shaping effect of diffractive phase optical elements designed by the hybrid algorithm is greatly improved. It will be widely used when the high uniformity is needed.